In the Jurafsky and Martin's Speech and Language Processing NLP textbook, a head tag in parse trees are mentioned that in lexicalized grammar, non-terminal in the tree is annotated with its lexical head.
I don't actually get what lexical heads are.

In the image attached, the word inside the parenthesis is the head word. What exactly are these and how do we determine them?
Lexical heads are a concept/idea in linguistics wherein each context-free rule has associated with it a "special" child (the lexical head) which is a central sub-constituent of the rule.
It is basically one word which represents the crux of the sentence.
They are determined by some additions to the set of parse rules. For example, the rules which determined the head words in your parse tree diagram are:
S => NP VP
VP => VBD NP PP
PP => P NP
NP => DT NN
etc. where the bold terms represent the head words.
As you can see, each constituent receives its headword from its head child. We basically find the parse tree for the sentence, assign head words for the leaf nodes and then propagate it upwards using these rules.
You can read about Head-Driven Phrase Structure Grammars to see where they are used.
(Reference)
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